In this paper, the insurance company invests its wealth in a capital market composed of a riskless asset and a risky asset. The aggregate claim process of the insurance company is modeled by the Gamma process so as to make it closer to the reality. In practice, the insurance company provides not only those policies with large lose coverings but also policies with small ones. The Gamma process can describe

In this paper we study approximations for the boundary crossing probabilities of moving sums of i.i.d. normal random variables. We approximate a discrete time problem with a continuous time problem allowing us to apply established theory for stationary Gaussian processes. By then subsequently correcting approximations for discrete time, we show that the developed approximations are very accurate even

In this paper, the periodic solutions of a stochastic two-prey one-predator model with impulsive perturbations in a polluted environment are focussed. The existence of global positive periodic solutions to the model are discussed by constructing the auxiliary system, and the sufficient conditions for the global attractivity of the periodic solutions are given by using Lyapunov method. An example is

We consider the time evolution of a lattice branching random walk with local perturbations. Under certain conditions, we prove the Carleman type estimation for the moments of a particle subpopulation number and show the existence of a steady state.

Probabilistic models for biological sequences (DNA and proteins) have many useful applications in bioinformatics. Normally, the values of parameters of these models have to be estimated from empirical data. However, even for the most common estimates, the maximum likelihood (ML) estimates, properties have not been completely explored. Here we assess the uniform accuracy of the ML estimates for models

We address the numerical solution of stochastic differential equations with multiplicative noise (SDEs) by means of balanced schemes. In particular, we study the design of balanced schemes that achieve the first order of weak convergence without involve the simulation of multiple stochastic integrals. We start by using the linear scalar SDE as a test problem to show that it is possible to construct

Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest. One of the statistical tools used to quantify the influence of each input variable on the quantity of interest are the Sobol’ sensitivity indices. In this paper, we consider

This paper studies an optimal excess-of-loss reinsurance and investment problem in a model with delay and jumps for an insurer, who can purchase excess-of-loss reinsurance and invest his surplus in a risk-free asset and a risky asset whose price is governed by a jump-diffusion model. The insurer’s surplus is described by a diffusion model, which is an approximation of the classical compound Poisson

Methods to obtain discrete analogs of continuous distributions have been widely applied in recent years. In general, the discretization process provides probability mass functions that can be competitive with traditional models used in the analysis of count data. The discretization procedure also avoids the use of continuous distribution to model strictly discrete data. In this paper, we propose two

The attractiveness of insurance saving products is driven by dividend payments to policyholders and participation in profits. These are mainly constrained by regulatory disposals on profit-sharing on the basis of statutory accounts. Moreover, since both prudential (Solvency II) and financial reporting (IFRS 17) regulations require market consistent best estimate measurement of insurance liabilities

In this paper, we investigate the reflected CIR process with two-sided jumps to capture the jump behavior and its non-negativeness. Applying the method of (complex) contour integrals, the closed-form solution to the joint Laplace transform of the first passage time crossing a lower level and the corresponding undershoot is derived. We further extend our arguments to the exit problem from a finite interval

Cure rate models have been used in a number of fields. These models are applied to analyze survival data when the population has a proportion of subjects insusceptible to the event of interest. In this paper, we propose a new cure rate survival model formulated under a competing risks setup. The number of competing causes follows the negative binomial distribution, while for the latent times we posit

The notion of generalized power function in the space of real symmetric matrices is used to introduce a kind of extended matrix-variate beta function. With the aid of this, we define a different versions of extended matrix-variate beta distributions. Some fundamental properties of these distributions are established. We show that using a linear transformation on the extended matrix-variate beta distributions

This paper studies a discrete-time batch arrival GI/Geo/1 queue where the server may take multiple vacations depending on the state of the queue/system. However, during the vacation period, the server does not remain idle and serves the customers with a rate lower than the usual service rate. The vacation time and the service time during working vacations are geometrically distributed. Keeping note

We investigate the joint distribution of nodes of small degrees and the degree profile in preferential dynamic attachment circuits. In particular, we study the joint asymptotic distribution of the number of the nodes of outdegree 0 (terminal nodes) and outdegree 1 in a very large circuit. The expectation and variance of the number of those two types of nodes are both asymptotically linear with respect

We prove a version of the reduction principle for functionals of vector long-range dependent random fields. The components of the fields may have different long-range dependent behaviours. The results are illustrated by an application to the first Minkowski functional of the Fisher–Snedecor random fields. Simulation studies confirm the obtained theoretical results and suggest some new problems.

We consider a classical risk process with arrival of claims following a non-stationary Hawkes process. We study the asymptotic regime when the premium rate and the baseline intensity of the claims arrival process are large, and claim size is small. The main goal of the article is to establish a diffusion approximation by verifying a functional central limit theorem and to compute the ruin probability

This article deals with single server queue with modified vacation policy. The modified vacation policy captures the operation of a close down period, type 1 vacation period, type 2 vacation period, a start-up period and a dormant period. Here, type 1 vacations takes a short period of random duration and type 2 vacation take a long period of random duration. Explicit expressions have been obtained

We present a new algorithm which detects the maximal possible number of matched disjoint pairs satisfying a given caliper when a bipartite matching is done with respect to a scalar index (e.g., propensity score), and constructs a corresponding matching. Variable width calipers are compatible with the technique, provided that the width of the caliper is a Lipschitz function of the index. If the observations

An accelerated life test (ALT) is commonly used in reliability studies of high quality products. A step-stress experiment is one such ALT that is often used in practice. In this paper, we develop exact inference based on likelihood-ratio test for a simple step-stress model with exponential lifetimes under Type-II censoring. We consider both unrestricted and order-restricted maximum likelihood estimators

In this paper, we study a new one-dimensional homogeneous stochastic process, termed the Square of the Brennan-Schwartz model, which is used in various contexts. We first establish the probabilistic characteristics of the model, such as the analytical expression solution to Itô’s stochastic differential equation, after which we determine the trend functions (conditional and non-conditional) and the

This paper proposes a block-structured Markov process to describe the spread of epidemics of Susceptible-Infected-Removed (SIR) type. Our purpose is to determine the distribution of the final state of the process and of some other interesting measures of the dimension of the epidemic. The followed modeling approach proves to be simple and systematic. Its flexibility is underlined by the presentation

We consider a single-server queueing system with server vacations as the important component of the polling queueing model of a real-world system. Period of continuous operation of the server (the maximum server attendance time) is restricted, but the service of a customer cannot be interrupted when this period expires. Such features are inherent for many real-world systems with resource sharing. We